Cost Function Research Articles

Optimal reorientation of planar floating snake robots with collision avoidance

In this paper, a motion planning algorithm for floating planar under-actuated hyper-redundant snake robots is proposed. The presented algorithm generates locally optimal shape trajectories, i.e., continuous trajectories in the base space of the robot. Such shape trajectories produce a desired rotation of the snake robot, i.e., change in the uncontrolled orientation fiber variable. The proposed method formulates the motion planning problem as an optimization problem where the objective function could be defined to minimize various metrics, such as energy-based cost functions. Additionally, the proposed motion planning algorithm uses a heuristic to generate shape trajectories that avoid self-intersections and obstacle collision. Hence, the motion planning method generates shape trajectories that locally minimize user-defined cost functions and eliminate self-intersections or obstacle collision. The proposed gait generation method is validated using numerical simulations of five-link and seven-link snake robots.

On optimal control at the onset of a new viral outbreak

We propose a versatile model with a flexible choice of control for an early-pandemic outbreak prevention when vaccine/drug is not yet available. At that stage, control is often limited to non-medical interventions like social distancing and other behavioral changes. For the SIR optimal control problem, we show that the running cost of control satisfying mild, practically justified conditions generates an optimal strategy, u(t), t ∈ [0, T], that is sustainable up until some moment τ ∈ [0, T). However, for any t ∈ [τ, T], the function u(t) will decline as t approaches T, which may cause the number of newly infected people to increase. So, the window from 0 to τ is the time for public health officials to prepare alternative mitigation measures, such as vaccines, testing, antiviral medications, and others. In addition to theoretical study, we develop a fast and stable computational method for solving the proposed optimal control problem. The efficiency of the new method is illustrated with numerical examples of optimal control trajectories for various cost functions and weights. Simulation results provide a comprehensive demonstration of the effects of control on the epidemic spread and mitigation expenses, which can serve as invaluable references for public health officials.

Inversion of 2D Magnetotelluric (MT) Data with Axial Anisotropy using Adaptive Particle Swarm Optimization (PSO)

In the presence of anisotropic resistivity structures, Magnetotelluric (MT) data inversion based on an isotropic resistivity model will be insufficient. Recent work on anisotropic MT inversions is primarily conducted using gradient-based, deterministic methods which may converge towards local minima and in general, suffer from ill-posedness of the inversion problem. Alternatively, meta-heuristical methods, such as Particle Swarm Optimization (PSO), are able to find the global minima of cost function. At the same time, they are easy to implement and do not require access to the dense Jacobian (and Hessian) matrix as needed by deterministic inversion methods. In this paper we propose PSO inversion for the anisotropic MT inversion problem using an adaptive inertia weights control strategy to balance exploration and exploitation during the PSO search. Higher order differential regularization is introduced with a Gaussian filter, where the conventional first order, Occam-like regularization term is replaced by a variance term. We investigate the performance of the proposed PSO inversion for an isotropic as well as an axial anisotropic synthetic case to demonstrate improvements over an Occam-like regularization. For the COPROD2 benchmark data set, the proposed PSO inversion can not only reproduce the extend of the North American Central Plains (NACP) conductive anomaly, but also to predict an anisotropy ratio of two orders of magnitude, which is in accordance with laboratory findings.

Parameter-setting heuristic for the quantum alternating operator ansatz

The quantum alternating operator ansatz (QAOA) is a generalized approach for solving challenging optimization problems that builds on the alternating structure of the quantum approximate optimization algorithm. Finding high-quality parameters efficiently for QAOA remains a major challenge in practice. In this work, we introduce a classical strategy for parameter setting, suitable for cases in which the number of distinct cost values grows only polynomially with the problem size, such as is common for constraint-satisfaction problems. The crux of our strategy is that we replace the cost function expectation value step of QAOA with a classical model that can be efficiently evaluated classically and has parameters which play an analogous role to the QAOA parameters. This model is based on empirical observations that, in some QAOA states, variable configurations with the same cost have the same amplitudes from step to step. We define this class of states as homogeneous states. For problems with particular symmetries, QAOA states are guaranteed to be homogeneous. More generally, high overlaps between QAOA states and homogeneous states have been empirically observed in a number of settings. Building on this idea, we define a classical homogeneous proxy for QAOA in which this property holds exactly and which yields information describing both states and expectation values. We then classically determine high-quality parameters for this proxy and then use these parameters in QAOA, an approach we label the homogeneous heuristic for parameter setting. We numerically examine this heuristic for MaxCut on unweighted Erdős-Rényi random graphs. For up to three QAOA levels we demonstrate that the heuristic is easily able to find parameters that match approximation ratios corresponding to previously found globally optimized approaches. For levels up to 20 we obtain parameters using our heuristic with approximation ratios monotonically increasing with depth, while a strategy that uses parameter transfer instead fails to converge with comparable classical resources. These results suggest that our heuristic may find good parameters in regimes that are intractable with noisy intermediate-scale quantum devices. Finally, we outline how our heuristic may be applied to wider classes of problems. Published by the American Physical Society 2024

A Dynamic Programming Approach to the Collision Avoidance of Autonomous Ships

The advancement of autonomous capabilities in maritime navigation has gained significant attention, with a trajectory moving from decision support systems to full autonomy. This push towards autonomy has led to extensive research focusing on collision avoidance, a critical aspect of safe navigation. Among the various possible approaches, dynamic programming is a promising tool for optimizing collision avoidance maneuvers. This paper presents a DP formulation for the collision avoidance of autonomous vessels. We set up the problem framework, formulate it as a multi-stage decision process, define cost functions and constraints focusing on the actual requirements a marine maneuver must comply with, and propose a solution algorithm leveraging parallel computing. Additionally, we present a greedy approximation to reduce algorithm complexity. We put the proposed algorithms to the test in realistic navigation scenarios and also develop an extensive test on a large set of randomly generated scenarios, comparing them with the RRT* algorithm using performance metrics proposed in the literature. The results show the potential benefits of an autonomous navigation or decision support framework.

Intelligent Vehicle Path Planning Based on Optimized A* Algorithm.

With the rapid development of the intelligent driving technology, achieving accurate path planning for unmanned vehicles has become increasingly crucial. However, path planning algorithms face challenges when dealing with complex and ever-changing road conditions. In this paper, aiming at improving the accuracy and robustness of the generated path, a global programming algorithm based on optimization is proposed, while maintaining the efficiency of the traditional A* algorithm. Firstly, turning penalty function and obstacle raster coefficient are integrated into the search cost function to increase the adaptability and directionality of the search path to the map. Secondly, an efficient search strategy is proposed to solve the problem that trajectories will pass through sparse obstacles while reducing spatial complexity. Thirdly, a redundant node elimination strategy based on discrete smoothing optimization effectively reduces the total length of control points and paths, and greatly reduces the difficulty of subsequent trajectory optimization. Finally, the simulation results, based on real map rasterization, highlight the advanced performance of the path planning and the comparison among the baselines and the proposed strategy showcases that the optimized A* algorithm significantly enhances the security and rationality of the planned path. Notably, it reduces the number of traversed nodes by 84%, the total turning angle by 39%, and shortens the overall path length to a certain extent.

Assessing CESM2 Clouds and Their Response to Climate Change Using Cloud Regimes

Abstract The Community Earth System Model, version 2 (CESM2), has a very high climate sensitivity driven by strong positive cloud feedbacks. To evaluate the simulated clouds in the present climate and characterize their response with climate warming, a clustering approach is applied to three independent satellite cloud products and a set of coupled climate simulations. Using k-means clustering with a Wasserstein distance cost function, a set of typical cloud configurations is derived for the satellite cloud products. Using satellite simulator output, the model clouds are classified into the observed cloud regimes in both current and future climates. The model qualitatively reproduces the observed cloud configurations in the historical simulation using the same time period as the satellite observations, but it struggles to capture the observed heterogeneity of clouds which leads to an overestimation of the frequency of a few preferred cloud regimes. This problem is especially apparent for boundary layer clouds. Those low-level cloud regimes also account for much of the climate response in the late twenty-first century in four shared socioeconomic pathway simulations. The model reduces the frequency of occurrence of these low-cloud regimes, especially in tropical regions under large-scale subsidence, in favor of regimes that have weaker cloud radiative effects.

Improved A* Algorithm for Path Planning Based on CubeSats In-Orbit Electromagnetic Transfer System

For future large-scale CubeSat applications in orbit, the deployer must accommodate a greater number of CubeSats and facilitate cluster releases. This paper introduces an improved A* algorithm tailored for CubeSat in-orbit transfer path planning. Unlike the traditional A* algorithm, this enhanced version incorporates a path coordination strategy to manage congestion caused by the simultaneous transfer of many CubeSats, ensuring they reach their designated release positions smoothly and thus significantly boosting the efficiency of CubeSat transfers. Additionally, the algorithm develops a cost model for attitude disturbances on the electromagnetic conveying platform and crafts an improved cost function. It strategically balances the reduction in attitude disturbances caused by CubeSat transfers with the efficiency of these transfers. The primary goal is to minimize platform disturbances while optimizing the number of steps CubeSats need to reach their intended positions. The effectiveness of this algorithm is demonstrated through detailed case studies, which confirm that during the CubeSat transfer process, the platform’s attitude remains stable, and the transfer efficiency is well-managed, achieving efficient path planning for the in-orbit transfer of numerous CubeSats.

Wind Power Integration and Challenges in Low Wind Zones. A Study Case: Albania

High wind performance systems are influenced by many factors such as site wind resources and configuration, technical wind turbine features and many financial conditions. Scenario planning and modelling activities often focus on restricted parameters and numbers to justify wind power plant performance. To better understand possible pathways to scaling up the distributed wind market in Albania, a deep and multidimensional calculations based on Monte Carlo analysis, using RETScreen and wind JEDI model, to assess socio-economic impact as a function of turbine output power, operating and maintenance cost and many other financial inputs by testing different WT (i.e., VESTAS, GAMESA, W2E and NORDEX) with rated power from 3.45 MW up to 4.5MW applied on LCOE, NPV, SPP, equity payback, B-C, after-tax IRR on equity and effects of GHG credits extended at a sensitivity range of ±35% is scientifically performed. From the simulation results LCOE reaches a minimal value of €43.48/MWh, if the debt rate is 99 % and a debt interest rate of 5.0%, a TotCapEx of €828/MW (-35 % less expenditures) indexed as the best scenario. For the base case scenario LCOE results €62.79/MWh, when applying a debt rate of 80% and a TotCapEx of (€1274/MW), while in the worst-case scenario LCOE impart a maximal value of €87.63/MWh if a TotCapEx of €1720/MW (+35 % more expenditures) and a share of 52 % debt rate is applied. Local annual economic impact (m€) during construction period and operating period evaluated in the wind JEDI model result around m€ 89.92 and m€ 23.54, respectively. As a conclusion, wind power plants (WPP), installed in low wind zones (Albania and many other EU countries) would be of interest if an electricity export rate of 110€/MWh, and a GHG credit rate of €50/tCO2 were accepted.

3D multi-object tracking based on informatic divergence-guided data association

In the existing literature, most 3D multi-object tracking algorithms based on the tracking-by-detection framework employed deterministic tracks and detections for similarity calculation in the data association stage. Namely, the inherent uncertainties existing in tracks and detections are overlooked. In this work, we discard the commonly used deterministic tracks and deterministic detections for data association, instead, we propose to model tracks and detections as random vectors in which uncertainties are taken into account. Then, based on a modified Kullback-Leibler divergence, the similarity between two multidimensional distributions, i.e. track and detection, is evaluated for data association purposes. Lastly, the level of track uncertainty is incorporated in our cost function design to guide the data association process. Comparative experiments have been conducted on two typical datasets, KITTI and nuScenes, and the results indicated that our proposed method outperformed the compared state-of-the-art 3D tracking algorithms. For the benefit of the community, our code has been made available at https://github.com/hejiawei2023/UG3DMOT.

Optimal control in models of virus propagation

Based on the SEIRD model, we consider that when multiple viruses of different virulence coexist, the more virulent virus will reinfect nodes already infected by the less virulent virus, which we call here Superexposed. Based on the state transitions, the corresponding differential equations and cost functions are established, then building the corresponding optimal control problem, where the vaccine efficiency and drug efficiency are controlled variables. This nonlinear optimal control problem is solved by Pontryagin’s maximum principle to finding the structure of the optimal control strategies. Based on the definition of the basic regeneration number, yielding the R0 value for the model, then discussed the final epidemic size. In the numerical analysis section, we validate the accuracy of the structure, fitting the behavior of each state and the effect of different parameter values.

Improving path planning for mobile robots in complex orchard environments: the continuous bidirectional Quick-RRT* algorithm.

Efficient obstacle-avoidance path planning is critical for orchards with numerous irregular obstacles. This paper presents a continuous bidirectional Quick-RRT* (CBQ-RRT*) algorithm based on the bidirectional RRT (Bi-RRT) and Quick-RRT* algorithms and proposes an expansion cost function that evaluates path smoothness and length to overcome the limitations of the Quick-RRT* algorithm for non-holonomic mobile robot applications. To improve the zigzag between dual trees caused by the dual-tree expansion of the Bi-RRT algorithm, CBQ-RRT* proposes the CreateConnectNode optimization method, which effectively solves the path smoothness problem at the junction of dual trees. Simulations conducted on the ROS platform showed that the CBQ-RRT* outperformed the unidirectional Quick-RRT* in terms of efficiency for various orchard layouts and terrain conditions. Compared to Bi-RRT*, CBQ-RRT* reduced the average path length and maximum heading angle by 8.5% and 21.7%, respectively. In addition, field tests confirmed the superior performance of the CBQ-RRT*, as evidenced by an average maximum path lateral error of 0.334m, a significant improvement over Bi-RRT* and Quick-RRT*. These improvements demonstrate the effectiveness of the CBQ-RRT* in complex orchard environments.

Modelling a Response of Complex-Phase Steel at High Strain Rates.

In this article, a response of the complex-phase high-strength steel SZBS800 was modelled by considering the strain-rate influence. The material's response was first measured with a series of standard tensile tests at lower strain rates. Higher strain rates were achieved using the unconventional test of shooting the ball into flat specimens. A viscoplastic formulation of the Cowper-Symonds material model was applied to consider the strain-rate effects. The parameters SIGY, p, and C of the material model were estimated using a step-wise procedure. First, rough estimates of the three parameters were obtained from the tensile tests using the grid search method. Then, the parameters p and C were fine-tuned using the reverse engineering approach. With the help of explicit dynamic simulations and all the experimental data, a multi-criteria cost function was defined and applied to obtain a smooth response function for the parameters p and C. Its optimum was determined by a real-valued genetic algorithm. The optimal values of the estimated parameters model the material response well, although a domain of optimum candidates spans two orders of magnitude for the parameter p and a few orders of magnitude for the parameter C.

Securing Internet-of-Medical-Things networks using cancellable ECG recognition

Reinforcement of the Internet of Medical Things (IoMT) network security has become extremely significant as these networks enable both patients and healthcare providers to communicate with each other by exchanging medical signals, data, and vital reports in a safe way. To ensure the safe transmission of sensitive information, robust and secure access mechanisms are paramount. Vulnerabilities in these networks, particularly at the access points, could expose patients to significant risks. Among the possible security measures, biometric authentication is becoming a more feasible choice, with a focus on leveraging regularly-monitored biomedical signals like Electrocardiogram (ECG) signals due to their unique characteristics. A notable challenge within all biometric authentication systems is the risk of losing original biometric traits, if hackers successfully compromise the biometric template storage space. Current research endorses replacement of the original biometrics used in access control with cancellable templates. These are produced using encryption or non-invertible transformation, which improves security by enabling the biometric templates to be changed in case an unwanted access is detected. This study presents a comprehensive framework for ECG-based recognition with cancellable templates. This framework may be used for accessing IoMT networks. An innovative methodology is introduced through non-invertible modification of ECG signals using blind signal separation and lightweight encryption. The basic idea here depends on the assumption that if the ECG signal and an auxiliary audio signal for the same person are subjected to a separation algorithm, the algorithm will yield two uncorrelated components through the minimization of a correlation cost function. Hence, the obtained outputs from the separation algorithm will be distorted versions of the ECG as well as the audio signals. The distorted versions of the ECG signals can be treated with a lightweight encryption stage and used as cancellable templates. Security enhancement is achieved through the utilization of the lightweight encryption stage based on a user-specific pattern and XOR operation, thereby reducing the processing burden associated with conventional encryption methods. The proposed framework efficacy is demonstrated through its application on the ECG-ID and MIT-BIH datasets, yielding promising results. The experimental evaluation reveals an Equal Error Rate (EER) of 0.134 on the ECG-ID dataset and 0.4 on the MIT-BIH dataset, alongside an exceptionally large Area under the Receiver Operating Characteristic curve (AROC) of 99.96% for both datasets. These results underscore the framework potential in securing IoMT networks through cancellable biometrics, offering a hybrid security model that combines the strengths of non-invertible transformations and lightweight encryption.

Smart Delivery Assignment through Machine Learning and the Hungarian Algorithm

Intelligent transportation and advanced mobility techniques focus on helping operators to efficiently manage navigation tasks in smart cities, enhancing cost efficiency, increasing security, and reducing costs. Although this field has seen significant advances in developing large-scale monitoring of smart cities, several challenges persist concerning the practical assignment of delivery personnel to customer orders. To address this issue, we propose an architecture to optimize the task assignment problem for delivery personnel. We propose the use of different cost functions obtained with deterministic and machine learning techniques. In particular, we compared the performance of linear and polynomial regression methods to construct different cost functions represented by matrices with orders and delivery people information. Then, we applied the Hungarian optimization algorithm to solve the assignment problem, which optimally assigns delivery personnel and orders. The results demonstrate that when used to estimate distance information, linear regression can reduce estimation errors by up to 568.52 km (1.51%) for our dataset compared to other methods. In contrast, polynomial regression proves effective in constructing a superior cost function based on time information, reducing estimation errors by up to 17,143.41 min (11.59%) compared to alternative methods. The proposed approach aims to enhance delivery personnel allocation within the delivery sector, thereby optimizing the efficiency of this process.

Identification of constitutive materials of bi-layer soft tissues from multimodal indentations

The personalisation of finite element models is an important problem in the biomechanical fields where subject-specific analyses are fundamental, particularly in studying soft tissue mechanics. The personalisation includes the choice of the constitutive law of the model's material, as well as the choice of the material parameters. In vivo identification of the material properties of soft tissues is challenging considering the complex behaviour of soft tissues that are, among other things, non-linear hyperelastic and heterogeneous. Hybrid experimental-numerical methods combining in vivo indentations and inverse finite element analyses are common to identify these material parameters. Yet, the uniqueness and the uncertainty of the multi-material hyperelastic model have not been evaluated. This study presents a sensitivity analysis performed on synthetic indentation data to investigate the identification uncertainties of the material parameters in a bi-material thigh phantom. Synthetic numerical data, used to replace experimental measurements, considered several measurement modalities: indenter force and displacement, stereo-camera 3D digital image correlation of the indented surface, and ultrasound B-mode images. A finite element model of the indentation was designed with either Ogden-Moerman or Mooney-Rivlin constitutive laws for both materials. The parameters' identifiability (i.e. the possibility of converging to a unique parameter set within an acceptable margin of error) was assessed with various cost functions formulated using the different synthetic data sets. The results underline the need for multiple experimental modalities to reduce the uncertainty of the identified parameters. Additionally, the experimental error can impede the identification of a unique parameter set, and the cost function depends on the constitutive law. This study highlights the need for sensitivity analyses before the design of the experimental protocol. Such studies can also be used to define the acceptable range of errors in the experimental measurement. Eventually, the impact of the evaluated uncertainty of the identified parameters should be further investigated according to the purpose of the finite element modelling.

Robust predictive control strategy of SCIG-based drive system

This article presents a robust finite control set predictive scheme for a stand-alone squirrel cage induction generator (SCIG) drive. This technique is considered an alternative to the drive system due to the inclusion of system nonlinearities and fast dynamic response. The control objective in the distributed generation environment is to fix the output voltage to follow the stand-alone requirement. The strategy establishes optimized switching instants for cost function minimization for both source and load converter control and diminished cross-coupling amid active and reactive power during transient scenarios. The scheme is designed to achieve the minimal effect caused by the parameter uncertainties. During source and load changes, this work will also address the maintenance of dc-link voltage, machine, and load variables at the set value, supported by machine and load-end converter control to achieve stand-alone load objectives. In addition, the presented scheme is also tested with random variation of speed to check the efficacy of the control configuration. The drive performance is evaluated by simulation using MATLAB/Simulink environment. Comprehensive real-time findings obtained from a scaled laboratory test bench using dSPACE-1104 are provided to verify the feasibility of the predictive solution.

Data-driven economic MPC with asymptotic stability and strong duality verification using Hankel matrix

We consider the problem of dynamic regulation with an economic cost function to control unknown linear systems, in which improving the economic performance and guaranteeing the stability of economical optimal equilibrium point are control objectives. A data-driven economic MPC scheme is presented using measured input-output trajectories without a prior system identification step. Our method uses Hankel matrices which include one input-output data trajectory for prediction in economic MPC, while persistently exciting of the input generating the data is needed. One of the novelties of the presented framework is directly verifying the strong duality property from input-output trajectory with the general cost function, considered as the supply rate. This is used to find a Lyapunov function for data-driven economic MPC. Under the strong duality assumption, asymptotic stability of the economical optimal equilibrium point for the closed-loop system with terminal equality constraint is guaranteed. The proposed data-driven economic MPC approach needs only persistently exciting data trajectory along with an upper bound on the system order and need no model description and no online parameter estimation. The proposed scheme applicability compared to the existing model-based economic MPC and data-driven MPC is illustrated for continuous stirred tank reactor (CSTR) and a numerical example and the robustness of the proposed scheme is evaluated in the case of measurement noise, as well as nonlinear model for CSTR system.

Shape optimization of annular transonic thrust nozzles via genetic algorithm and adjoint method

In this research, the idea of combining the genetic algorithm and adjoint method was proposed to leverage the benefits of both approaches to improve the accuracy of thrust nozzle shape optimization. Although the genetic algorithm can search the entire design space to approach the global optimum, its computational cost increases considerably with the number of design variables. Meanwhile, the adjoint method is unaffected by the design variables, but it cannot achieve the global optimum directly and relies on the initial guess geometry. To address these challenges, a genetic algorithm was initially employed to approximate the global optimal geometry of a thrust nozzle with a conical center body parameterized by a Bezier curve. A MATLAB code integrated the geometry parameterization, genetic algorithm, and Fluent R2 2021 flow solver. The resulting geometry was then considered as the initial guess for the adjoint method, which accurately achieved the final optimal geometry with increased control points. The genetic algorithm aimed to maximize the thrust coefficient as the objective function, while the adjoint solver aimed to minimize the axial velocity variance at the nozzle outlet as the cost function. Three distinct constraints were incorporated in the optimization process, and the influence of the center body shape on the results was thoroughly examined to consider all possible geometries throughout the optimization procedure. The findings revealed that the conical center body effectively adjusted the flow angle at the exit, significantly affecting the thrust force. Both optimization steps reduced the average velocity and increased the average pressure at the nozzle exit, enhanced the mass flow rate, and finally increased the thrust force. The genetic algorithm and adjoint method contributed to 3 % and 0.6 % increases, respectively, in the thrust force, resulting in a thrust coefficient of 96.15 % for the final optimized nozzle.

Strategic Behavior and Optimal Inventory Level in a Make-to-Stock Queueing System with Retrial Customers

In this article, we consider a make-to-stock queueing system with retrial customers. Upon their arrival, customers make a decision to either join the system or not based on a reward–cost function. If customers join the retrial queue, they become repeat customers. Each repeat customer repeats their demand after an exponential amount of time until they have been successfully served. We explore the equilibrium strategies of customers in both the almost observable and unobservable cases. Furthermore, we also analyze the expected costs of the entire system based on the customers’ behavior in these two cases. Additionally, we determine the optimal inventory levels in both cases through numerical experiments.